exp-form property (was Taylor series of elliptic_kc(m) about m=0 fails with error)

On Fri, Sep 28, 2012 at 7:24 AM, David Billinghurst <dbmaxima at gmail.com>wrote:

> On 18/09/2012 8:30 PM, David Billinghurst wrote:
>
>> Taylor series of elliptic_kc(m) about m=0 fails with
>> maxima-5.28.0/gcl/windows and clisp/windows.
>>
>> taylor(elliptic_kc(m),m,0,1);
>>
>> Maxima encountered a Lisp error:
>>  Error in MACSYMA-TOP-LEVEL [or a callee]: Bind stack overflow.
>> Automatically continuing.
>> To enable the Lisp debugger set *debugger-hook* to nil.
>>
>> According to A&S 17.3.11
>>
>> K(m) ~= 1 + (1/2)^2 m + (1.3/2.4)^2 m^2 + ....
>>
>
> I have been having a look at this problem.   I seem to be able to define a
> separate Taylor series about 0 using the exp-form property, without
> breaking the existing definition.  The exp-form function is defined for
> some trig and exponential functions in hayat.lisp.  Just borrowing the
> expression for sin, as a proof of concept, I see
>
> (%i2) :lisp (get '%sin 'exp-form)
> (EXPEXP-FUNS ((1 . 1) 1 . 1) (-1 . 1) (-1 . 1) (2 . 1))
>
> (%i2) :lisp (putprop '%elliptic_kc (get '%sin 'exp-form) 'exp-form)
> (EXPEXP-FUNS ((1 . 1) 1 . 1) (-1 . 1) (-1 . 1) (2 . 1))
>
> (%i4) taylor(elliptic_kc(x),x,0,4);
>                                      3
>                                     x
> (%o4)/T/                        x - -- + . . .
>                                     6
>
> and taylor(elliptic_kc(x),x,0,4) still works.  I don't think this is
> useable for series about x # 0 or for multivariate functions.
>

Presumably you meant the taylor series at some point other than 0 here.

This is interesting.  I haven't had a chance to try it out, but I was
thinking of modifying taylor so that if there was a powerseries or
deftaylor form (the sp2 property is set), then taylor would check to see if
the expansion was at 0 or not.  If so, then the deftaylor form could be
used.  If not, then taylor would continue as if deftaylor didn't exist.

I think this would make sense since deftaylor says the expansion is always
about 0.

Ray